Two-sided estimates for the approximation numbers of Hardy-type operators in L∞ and L¹

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Abstract

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In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator T:Lp(ℝ+)→Lp(ℝ+) defined by (Tf)(x)≔v(x)ʃ0∞u(t)f(t)dt when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].